BIFURCATION IN CROSS-EQUATORIAL AIR-FLOW - A NONLINEAR CHARACTERISTICOF LAGRANGIAN MODELING

Low-level monsoonal cross-equatorial airflow is investigated using a s imple Lagrangian model for the tropical atmosphere. With the use of Ja cobian elliptic functions, analytical solutions for the dynamic system are obtained to an extent that enables the most interesting features of the model to be demonstrated. It is found that there exists some un predictability with the equatorial airflow, in the sense that the traj ectory of the airflow can either remain in one hemisphere or cross the equator from one hemisphere to another depending upon the value of a model parameter lambda(c) being negative or positive, even when the co rresponding external forcings are of little difference. By means of qu alitative analysis of the dynamic system, some more esoteric propertie s of the model solutions are investigated. It is found that the model exhibits a very interesting bifurcation, which explains the unpredicta bility. The bifurcation is a characteristic attributable to the nonlin earity of the Coriolis term in the Lagrangian model. Since the Corioli s term is linear in a dynamically identical Eulerian model, the charac teristic would not be explicitly revealed by Eulerian modeling. By num erical method, the model is extended and applied to the simulation of cross-equatorial airflow in the context of Australian monsoon. The exe rcise provides an example of how to bridge the gap between a simplifie d analytical model and the realities of the actual tropical meteorolog y.